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          kd树练习:最近距离查询
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        <p>k-d就是k个维度，k-d树其实就是用不同的维度来对点集进行划分，从而达到快速查找的目的。 <span id="more"></span> 时间复杂度比较科学的方法，一般是算出点集在某个维度上的方差，然后选择方差最大的维度，对点集进行划分，但是由于涉及到double的运算，有时在时间复杂度上并不尽如人意。所以轮换维度进行分割的方法也比较常见。 k-d树最简单的应用，就是查询在一个点集中，离一个点最近的点是哪个。 其实就是设定一个距离，然后不断的查找k-d树的子树，以查询点为圆心的圆会随着查询，逐渐的缩小。 这个查询的最差时间复杂度是<span class="math inline">\(O(\sqrt n)\)</span>，平均的时间复杂度大概是<span class="math inline">\(O(log(n))\)</span>。 <a target="_blank" rel="noopener" href="http://acm.hdu.edu.cn/showproblem.php?pid=2966">http://acm.hdu.edu.cn/showproblem.php?pid=2966</a> 裸的kd树，求每个点到点集的最近点</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> INT_INF 0x3fffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> LL_INF 0x3fffffffffffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> EPS 1e-12</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> MOD 1000000007</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> PI 3.141592653579798</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> N 600000</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">long</span> LL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span> ULL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">double</span> DB;</span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">data</span></span></span><br><span class="line"><span class="class">&#123;</span></span><br><span class="line">    LL pos[<span class="number">10</span>];</span><br><span class="line">    <span class="keyword">int</span> id;</span><br><span class="line">&#125; T[N] , op , point;</span><br><span class="line">data W[N];</span><br><span class="line"><span class="keyword">int</span> split[N],now,n,demension;</span><br><span class="line"></span><br><span class="line"><span class="keyword">bool</span> use[N];</span><br><span class="line">LL ans,id;</span><br><span class="line">DB var[<span class="number">10</span>];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">cmp</span><span class="params">(data a,data b)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> a.pos[split[now]]&lt;b.pos[split[now]];</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">build</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> pos=<span class="number">0</span>;pos&lt;demension;pos++)</span><br><span class="line">    &#123;</span><br><span class="line">        DB ave=var[pos]=<span class="number">0.0</span>;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            ave+=T[i].pos[pos];</span><br><span class="line">        ave/=(R-L+<span class="number">1</span>);</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            var[pos]+=(T[i].pos[pos]-ave)*(T[i].pos[pos]-ave);</span><br><span class="line">        var[pos]/=(R-L+<span class="number">1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    split[now=mid]=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;demension;i++)</span><br><span class="line">        <span class="keyword">if</span>(var[split[mid]]&lt;var[i]) split[mid]=i;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">nth_element</span>(T+L,T+mid,T+R+<span class="number">1</span>,cmp);</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">build</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    <span class="built_in">build</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">query</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    LL dis=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i&lt;demension;i++)</span><br><span class="line">        dis+=(op.pos[i]-T[mid].pos[i])*(op.pos[i]-T[mid].pos[i]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(!use[T[mid].id] &amp;&amp; dis&lt;ans)</span><br><span class="line">    &#123;</span><br><span class="line">        ans=dis;</span><br><span class="line">        point=T[mid];  </span><br><span class="line">        id=T[mid].id;  </span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">   </span><br><span class="line">    LL radius=(op.pos[split[mid]]-T[mid].pos[split[mid]])*(op.pos[split[mid]]-T[mid].pos[split[mid]]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(op.pos[split[mid]]&lt;T[mid].pos[split[mid]])</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">else</span></span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">work</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;n);</span><br><span class="line">    demension=<span class="number">2</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j&lt;demension;j++)</span><br><span class="line">            <span class="built_in">scanf</span>(<span class="string">&quot;%lld&quot;</span>,&amp;T[i].pos[j]);</span><br><span class="line">        T[i].id=i;</span><br><span class="line">        W[i]=T[i];</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">build</span>(<span class="number">1</span>,n);  </span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> m,q;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> q=<span class="number">1</span>;q&lt;=n;q++)</span><br><span class="line">    &#123;</span><br><span class="line">        op=W[q];</span><br><span class="line">        use[q]=<span class="number">1</span>;</span><br><span class="line">        ans=(((LL)INT_INF)*INT_INF);</span><br><span class="line">        <span class="built_in">query</span>(<span class="number">1</span>,n);</span><br><span class="line">        use[q]=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%lld\n&quot;</span>,ans);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">int</span> T;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;T);</span><br><span class="line">    <span class="keyword">while</span>(T--) <span class="built_in">work</span>();</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p><a target="_blank" rel="noopener" href="http://acm.hdu.edu.cn/showproblem.php?pid=4347">http://acm.hdu.edu.cn/showproblem.php?pid=4347</a> 裸，求最近的m个点</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> INT_INF 0x3fffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> LL_INF 0x3fffffffffffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> EPS 1e-12</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> MOD 1000000007</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> PI 3.141592653579798</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> N 60000</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">long</span> LL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span> ULL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">double</span> DB;</span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">data</span></span></span><br><span class="line"><span class="class">&#123;</span></span><br><span class="line">    LL pos[<span class="number">10</span>];</span><br><span class="line">    <span class="keyword">int</span> id;</span><br><span class="line">&#125; T[N] , op , point;</span><br><span class="line"><span class="keyword">int</span> split[N],now,n,demension;</span><br><span class="line"></span><br><span class="line"><span class="keyword">bool</span> use[N];</span><br><span class="line">LL ans,id;</span><br><span class="line">DB var[<span class="number">10</span>];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">cmp</span><span class="params">(data a,data b)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> a.pos[split[now]]&lt;b.pos[split[now]];</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">build</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> pos=<span class="number">0</span>;pos&lt;demension;pos++)</span><br><span class="line">    &#123;</span><br><span class="line">        DB ave=var[pos]=<span class="number">0.0</span>;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            ave+=T[i].pos[pos];</span><br><span class="line">        ave/=(R-L+<span class="number">1</span>);</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            var[pos]+=(T[i].pos[pos]-ave)*(T[i].pos[pos]-ave);</span><br><span class="line">        var[pos]/=(R-L+<span class="number">1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    split[now=mid]=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;demension;i++)</span><br><span class="line">        <span class="keyword">if</span>(var[split[mid]]&lt;var[i]) split[mid]=i;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">nth_element</span>(T+L,T+mid,T+R+<span class="number">1</span>,cmp);</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">build</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    <span class="built_in">build</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">query</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    LL dis=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i&lt;demension;i++)</span><br><span class="line">        dis+=(op.pos[i]-T[mid].pos[i])*(op.pos[i]-T[mid].pos[i]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(!use[T[mid].id] &amp;&amp; dis&lt;ans)</span><br><span class="line">    &#123;</span><br><span class="line">        ans=dis;</span><br><span class="line">        point=T[mid];</span><br><span class="line">        id=T[mid].id;</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    LL radius=(op.pos[split[mid]]-T[mid].pos[split[mid]])*(op.pos[split[mid]]-T[mid].pos[split[mid]]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(op.pos[split[mid]]&lt;T[mid].pos[split[mid]])</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">else</span></span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">while</span>(<span class="built_in">scanf</span>(<span class="string">&quot;%d%d&quot;</span>,&amp;n,&amp;demension)!=EOF)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j&lt;demension;j++)</span><br><span class="line">                <span class="built_in">scanf</span>(<span class="string">&quot;%I64d&quot;</span>,&amp;T[i].pos[j]);</span><br><span class="line">            T[i].id=i;</span><br><span class="line">        &#125;</span><br><span class="line">        </span><br><span class="line">        <span class="built_in">build</span>(<span class="number">1</span>,n);</span><br><span class="line"></span><br><span class="line">        <span class="keyword">int</span> m,q; <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;q);</span><br><span class="line">        <span class="keyword">while</span>(q--)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="built_in">memset</span>(use,<span class="number">0</span>,<span class="built_in"><span class="keyword">sizeof</span></span>(use));</span><br><span class="line">            </span><br><span class="line">            <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i&lt;demension;i++)</span><br><span class="line">                <span class="built_in">scanf</span>(<span class="string">&quot;%I64d&quot;</span>,&amp;op.pos[i]);</span><br><span class="line">            <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;m);</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;the closest %d points are:\n&quot;</span>,m);</span><br><span class="line">            <span class="keyword">while</span>(m--)</span><br><span class="line">            &#123;</span><br><span class="line">                ans=(((LL)INT_INF)*INT_INF);</span><br><span class="line">                <span class="built_in">query</span>(<span class="number">1</span>,n);</span><br><span class="line">                <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i&lt;demension;i++)</span><br><span class="line">                &#123;</span><br><span class="line">                    <span class="built_in">printf</span>(<span class="string">&quot;%I64d&quot;</span>,point.pos[i]);</span><br><span class="line">                    <span class="keyword">if</span>(i==demension<span class="number">-1</span>) <span class="built_in">printf</span>(<span class="string">&quot;\n&quot;</span>);</span><br><span class="line">                    <span class="keyword">else</span> <span class="built_in">printf</span>(<span class="string">&quot; &quot;</span>);</span><br><span class="line">                &#125;</span><br><span class="line">                use[id]=<span class="number">1</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>http://acm.hdu.edu.cn/showproblem.php?pid=5992 今年青岛的原题，确实很裸。</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br><span class="line">160</span><br><span class="line">161</span><br><span class="line">162</span><br><span class="line">163</span><br><span class="line">164</span><br><span class="line">165</span><br><span class="line">166</span><br><span class="line">167</span><br><span class="line">168</span><br><span class="line">169</span><br><span class="line">170</span><br><span class="line">171</span><br><span class="line">172</span><br><span class="line">173</span><br><span class="line">174</span><br><span class="line">175</span><br><span class="line">176</span><br><span class="line">177</span><br><span class="line">178</span><br><span class="line">179</span><br><span class="line">180</span><br><span class="line">181</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> INT_INF 0x3fffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> LL_INF 0x3fffffffffffffff</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> EPS 1e-12</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> MOD 1000000007</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> PI 3.141592653579798</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> N 200010</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> mk make_pair</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> pb push_back</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">long</span> LL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span> ULL;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">double</span> DB;</span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">data</span></span></span><br><span class="line"><span class="class">&#123;</span></span><br><span class="line">    LL pos[<span class="number">10</span>];</span><br><span class="line">    <span class="keyword">int</span> id;</span><br><span class="line">    LL c;</span><br><span class="line">&#125; T[N] , op , point;</span><br><span class="line"><span class="keyword">int</span> split[N],now,n,demension;</span><br><span class="line">data W[N];</span><br><span class="line"><span class="keyword">bool</span> use[N];</span><br><span class="line">LL ans,id;</span><br><span class="line">DB var[<span class="number">10</span>];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">cmp</span><span class="params">(data a,data b)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> a.pos[split[now]]&lt;b.pos[split[now]];</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">build</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> pos=<span class="number">0</span>;pos&lt;demension;pos++)</span><br><span class="line">    &#123;</span><br><span class="line">        DB ave=var[pos]=<span class="number">0.0</span>;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            ave+=T[i].pos[pos];</span><br><span class="line">        ave/=(R-L+<span class="number">1</span>);</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=L;i&lt;=R;i++)</span><br><span class="line">            var[pos]+=(T[i].pos[pos]-ave)*(T[i].pos[pos]-ave);</span><br><span class="line">        var[pos]/=(R-L+<span class="number">1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    split[now=mid]=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;demension;i++)</span><br><span class="line">        <span class="keyword">if</span>(var[split[mid]]&lt;var[i]) split[mid]=i;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">nth_element</span>(T+L,T+mid,T+R+<span class="number">1</span>,cmp);</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">build</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    <span class="built_in">build</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">query</span><span class="params">(<span class="keyword">int</span> L,<span class="keyword">int</span> R)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(L&gt;R) <span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">int</span> mid=(L+R)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    </span><br><span class="line">    LL dis=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i&lt;demension;i++)</span><br><span class="line">        dis+=(op.pos[i]-T[mid].pos[i])*(op.pos[i]-T[mid].pos[i]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(!use[T[mid].id] &amp;&amp; dis&lt;ans)</span><br><span class="line">    &#123;</span><br><span class="line">        ans=dis;</span><br><span class="line">        point=T[mid];  </span><br><span class="line">        id=T[mid].id;  </span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span>(!use[T[mid].id] &amp;&amp; dis==ans &amp;&amp; id&gt;T[mid].id)</span><br><span class="line">    &#123;</span><br><span class="line">        point=T[mid];  </span><br><span class="line">        id=T[mid].id;  </span><br><span class="line">    &#125;</span><br><span class="line">    LL radius=(op.pos[split[mid]]-T[mid].pos[split[mid]])*(op.pos[split[mid]]-T[mid].pos[split[mid]]);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">if</span>(op.pos[split[mid]]&lt;T[mid].pos[split[mid]])</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">else</span></span><br><span class="line">    &#123;</span><br><span class="line">        <span class="built_in">query</span>(mid+<span class="number">1</span>,R);</span><br><span class="line">        <span class="keyword">if</span>(radius&lt;=ans) <span class="built_in">query</span>(L,mid<span class="number">-1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line">vector&lt;pair&lt;LL,<span class="keyword">int</span>&gt; &gt; pp;</span><br><span class="line">data an[N];</span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">cmp1</span><span class="params">(data a,data b)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> a.c&gt;b.c;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">cmp2</span><span class="params">(pair&lt;LL,<span class="keyword">int</span>&gt; a,pair&lt;LL,<span class="keyword">int</span>&gt; b)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> a&gt;b;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">work</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    pp.<span class="built_in">clear</span>();</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;n);</span><br><span class="line">    <span class="keyword">int</span> m,q; </span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;q);</span><br><span class="line">    demension=<span class="number">2</span>;</span><br><span class="line">    </span><br><span class="line">   <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j&lt;demension;j++)</span><br><span class="line">            <span class="built_in">scanf</span>(<span class="string">&quot;%lld&quot;</span>,&amp;T[i].pos[j]);</span><br><span class="line">        T[i].id=i;</span><br><span class="line">        <span class="built_in">scanf</span>(<span class="string">&quot;%lld&quot;</span>,&amp;T[i].c);</span><br><span class="line">        pp.<span class="built_in">pb</span>(<span class="built_in">mk</span>(T[i].c,i));</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">sort</span>(pp.<span class="built_in">begin</span>(),pp.<span class="built_in">end</span>(),cmp2);</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">build</span>(<span class="number">1</span>,n);</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=q;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j&lt;demension;j++)</span><br><span class="line">            <span class="built_in">scanf</span>(<span class="string">&quot;%lld&quot;</span>,&amp;W[i].pos[j]);</span><br><span class="line">        W[i].id=i;</span><br><span class="line">        <span class="built_in">scanf</span>(<span class="string">&quot;%lld&quot;</span>,&amp;W[i].c);</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">sort</span>(W+<span class="number">1</span>,W+q+<span class="number">1</span>,cmp1);</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">memset</span>(use,<span class="number">0</span>,<span class="built_in"><span class="keyword">sizeof</span></span>(use));</span><br><span class="line">    <span class="keyword">int</span> la=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=q;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">while</span>(pp[la].first&gt;W[i].c&amp;&amp;la!=pp.<span class="built_in">size</span>())</span><br><span class="line">        &#123;</span><br><span class="line">            use[pp[la].second]=<span class="number">1</span>;</span><br><span class="line">            la++;</span><br><span class="line">        &#125;</span><br><span class="line">        op=W[i];</span><br><span class="line">        <span class="comment">/*for(int j=0;j&lt;demension;j++)</span></span><br><span class="line"><span class="comment">        &#123;</span></span><br><span class="line"><span class="comment">            printf(&quot;%lld&quot;,W[i].pos[j]);</span></span><br><span class="line"><span class="comment">            printf(&quot; &quot;);</span></span><br><span class="line"><span class="comment">        &#125;</span></span><br><span class="line"><span class="comment">        printf(&quot;%lld **\n&quot;,W[i].c);*/</span></span><br><span class="line">        ans=(((LL)INT_INF)*INT_INF);</span><br><span class="line">        <span class="built_in">query</span>(<span class="number">1</span>,n);</span><br><span class="line">        an[W[i].id]=point;</span><br><span class="line">        <span class="comment">/*cout&lt;&lt;ans&lt;&lt;endl;</span></span><br><span class="line"><span class="comment">        for(int j=0;j&lt;demension;j++)</span></span><br><span class="line"><span class="comment">        &#123;</span></span><br><span class="line"><span class="comment">            printf(&quot;%lld&quot;,point.pos[j]);</span></span><br><span class="line"><span class="comment">            printf(&quot; &quot;);</span></span><br><span class="line"><span class="comment">        &#125;</span></span><br><span class="line"><span class="comment">        printf(&quot;%lld *\n&quot;,point.c);*/</span></span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=q;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j&lt;demension;j++)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%lld&quot;</span>,an[i].pos[j]);</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot; &quot;</span>);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%lld\n&quot;</span>,an[i].c);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">int</span> T;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;T);</span><br><span class="line">    <span class="keyword">while</span>(T--) <span class="built_in">work</span>();</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

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